B. D. O. Anderson and J. B. Moore. Optimal Filtering. Prentice-Hall, Englewood Cliffs, NJ, 1979. Home/Search Document Not in Database Summary Related Articles Check |
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Wiener Design of Adaptation Algorithms with.. - Sternad, Lindbom.. (2002) (Correct)
.... P k = lim P t kjt = lim E h t kjt h t kjt ; 5) where the expectation is taken with respect to e t in (3) and v t in (1) Among all adaptation laws which perform linear operations on y t , the Kalman lter will minimize P t kjt if t ; H(q ) and R e in (1) 3) are known [4, 18]. Kalman estimators are based on a state space model of (3) with (1) as the measurement equation. Kalman based adaptive lters discussed in the literature are mostly based on rst order autoregressive parameter models [14, 15, 10, 36] but can, of course, be designed for more complicated linear ....
B. D. O. Anderson and J. B. Moore, Optimal Filtering. Prentice Hall, Englewood Cli s, NJ, 1979.
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....j k ] be a Toeplitz matrix. The problem of solving the system of linear equations Mx = b is important in many areas of pure and applied mathematics: orthogonal polynomials, Pade approximation, signal processing, linear filtering, linear prediction and time series analysis. See, for instance, [1, 3, 15, 20, 21, 23, 24]. There are several fast, O(n ) algorithms # This manuscript incorporates minor corrections into the paper that appears in Rational Approximation and its Applications in Mathematics and Physics (J. Gilewicz, M. Pindor and W. Siemaszko, editors) Lecture Notes in Mathematics 1237, ....
B. D. O. Anderson and J. B. Moore, Optimal Filtering, Prentice-Hall, Englewood Cli#s, NJ, 1979.
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....the disturbing noise v(n) provided that the model parameter set fa(n) b(n) oe u (n) oe w (n)g is known. The Kalman filter order as given by the (d 1 q) Theta (d 1 q) state matrix F may be reduced by a suitable transformation of the state vector or of the observation signal y(n) [2]. Unfortunately, the reduced order Kalman filter needs a more complicated Kalman gain vector update. Thus, we decided to stick to the increased order Kalman filter. In most practical situations, the order increase is small because the order q of the disturbing noise model is much less than the ....
.... (n) s (1:d) n) v(n) b (n) v(n) v (1:q Gamma1) n) 11) yields from (10) e(n) y(n) Gamma s (1) n) Gamma v (1) n) s(n 1) s(n) k s (n)e(n) v(n 1) v(n) k v (n)e(n) s(n Gamma d) s (d 1) n) 12) The standard Kalman equations as given e.g. in [2] can be brought into a computationally efficient form by using the above notational convention and a block form of the (d 1 q) Theta(d 1 q) error covariance matrix P(n) S(n) X(n) n) V(n) n)S (1:p;1:d) n) e S(n) 1:p) n)a(n) oe u (n) p p(n) S (1:d;1:d) n) ....
B. D. O. Anderson, J. B. Moore, "Optimal filtering", Chapters 7, 11, Prentice-Hall, Inc., 1979.
Stochastic Mapping Frameworks - Richard Rikoski John (2002) (2 citations) (Correct)
....filter, the previous state estimate is replaced by the prediction. The terms in the projection Jacobian F x corresponding to static states are the identity matrix, meaning those terms are unchanged. A fixed lag Kalman smoother uses future information to refine its estimate of past states [1]. During projection, state estimates within the lag interval are treated as static terms, in a similar manner to static features in conventional stochastic mapping; they are not changed. However, the state which is one timestep too old is automatically discarded through a clever matrix operation. ....
B. D. O. Anderson and J. B. Moore. Optimal filtering. Englewood Cli#s, N.J.: Prentice-Hall, 1979.
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B. D. O. Anderson and J. B. Moore. Optimal Filtering. Prentice-Hall, Englewood Cliffs, NJ, 1979.
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Anderson, B. D. O., and J. B. Moore, Optimal Filtering. Englewood Cliffs, NJ: PrenticeHall, 1979.
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